Regression Project – Group 3 (Intermediate Report)

Reema and Muzammil

1. Introduction

  • The aim of this intermediate report is to explore determinants of income in South Austria.
  • We focus on data management and descriptive statistics before conducting regression modelling.
  • The response variable is net employment income (py010n).
  • Explanatory variables include gender, citizenship, household size, and age.
  • For the intermediate report we restrict to data management and descriptive statistics.

2. Data collection and description

  • Source: EU-SILC (European Union Statistics on Income and Living Conditions), Austria.
  • Type of data: survey data, representative sample of private households.
  • Data format: cross-sectional microdata with social, demographic, and income information.
  • Variables used:
    • py010n — employment income (numeric)
    • age — age in years (numeric)
    • hsize — household size (categorical converted to numeric)
    • gender — male / female (categorical)
    • citizenship — grouped nationality categories (categorical)
    • region — Austrian federal region
  • Missing value handling:
    • Keep only positive values of income (py010n > 0)
    • Convert hsize to numeric
    • Remove observations with missing values
  • Subsetting:
    • Only individuals living in Styria and Carinthia (South Austria, NUTS-1 region)

3. Load packages

options(repos = c(CRAN = "https://cloud.r-project.org"))
install.packages("simFrame")

The downloaded binary packages are in
    /var/folders/15/4lrzl3dn20j0wzcv5vd_8b4c0000gn/T//RtmpJsnaVQ/downloaded_packages
install.packages("dplyr")

The downloaded binary packages are in
    /var/folders/15/4lrzl3dn20j0wzcv5vd_8b4c0000gn/T//RtmpJsnaVQ/downloaded_packages
install.packages("ggplot2")

The downloaded binary packages are in
    /var/folders/15/4lrzl3dn20j0wzcv5vd_8b4c0000gn/T//RtmpJsnaVQ/downloaded_packages
install.packages("tidyr")

The downloaded binary packages are in
    /var/folders/15/4lrzl3dn20j0wzcv5vd_8b4c0000gn/T//RtmpJsnaVQ/downloaded_packages
install.packages("forcats")

The downloaded binary packages are in
    /var/folders/15/4lrzl3dn20j0wzcv5vd_8b4c0000gn/T//RtmpJsnaVQ/downloaded_packages
install.packages("effects")

The downloaded binary packages are in
    /var/folders/15/4lrzl3dn20j0wzcv5vd_8b4c0000gn/T//RtmpJsnaVQ/downloaded_packages
library(simFrame)
library(dplyr)        # data manipulation
library(ggplot2)      # visualization
library(tidyr)        # data tidying
library(forcats)      # factor management
library(effects)      # effect plots

4. Load data and select variables

data(eusilcP)
dat = eusilcP
str(eusilcP)  
'data.frame':   58654 obs. of  28 variables:
 $ hid        : int  1 1 2 2 3 4 4 4 5 6 ...
 $ region     : Ord.factor w/ 9 levels "Burgenland"<"Lower Austria"<..: 6 6 5 5 5 6 6 6 3 2 ...
 $ hsize      : Factor w/ 9 levels "1","2","3","4",..: 2 2 2 2 1 3 3 3 1 5 ...
 $ eqsize     : num  1.5 1.5 1.5 1.5 1 1.8 1.8 1.8 1 2.6 ...
 $ eqIncome   : num [1:58654(1d)] 11128 11128 19695 19695 5066 ...
  ..- attr(*, "dimnames")=List of 1
  .. ..$ : chr [1:58654] "2592313" "2592313" "2045000" "2045000" ...
 $ pid        : int  1 2 1 2 1 1 2 3 1 1 ...
 $ id         : chr  "0000101" "0000102" "0000201" "0000202" ...
 $ age        : num  25 24 57 53 30 32 33 8 77 34 ...
 $ gender     : Factor w/ 2 levels "male","female": 1 2 2 1 2 1 2 1 2 2 ...
 $ ecoStat    : Factor w/ 7 levels "1","2","3","4",..: 1 4 1 1 6 1 1 NA 5 2 ...
 $ citizenship: Factor w/ 3 levels "AT","EU","Other": 3 1 1 1 1 1 1 NA 1 1 ...
 $ py010n     : num  16693 0 0 16884 0 ...
 $ py050n     : num  0 0 12565 0 0 ...
 $ py090n     : num  0 0 0 0 5066 ...
 $ py100n     : num  0 0 0 0 0 ...
 $ py110n     : num  0 0 0 0 0 0 0 NA 0 0 ...
 $ py120n     : num  0 0 0 0 0 0 0 NA 0 0 ...
 $ py130n     : num  0 0 0 0 0 0 0 NA 0 0 ...
 $ py140n     : num  0 0 0 0 0 0 0 NA 0 0 ...
 $ hy040n     : num  0 0 0 0 0 0 0 0 0 0 ...
 $ hy050n     : num  0 0 0 0 0 ...
 $ hy070n     : num  0 0 0 0 0 0 0 0 0 0 ...
 $ hy080n     : num  0 0 0 0 0 0 0 0 0 0 ...
 $ hy090n     : num  0 0 0 0 0 ...
 $ hy110n     : num  0 0 0 0 0 ...
 $ hy130n     : num  0 0 93.6 93.6 0 ...
 $ hy145n     : num  0 0 -187 -187 0 ...
 $ main       : logi  TRUE FALSE FALSE TRUE TRUE TRUE ...
head(eusilcP)
summary(eusilcP)
      hid                  region          hsize           eqsize     
 Min.   :    1   Vienna       :11657   2      :14128   Min.   :1.000  
 1st Qu.: 6262   Lower Austria:11127   4      :13180   1st Qu.:1.500  
 Median :12465   Upper Austria:10310   3      :12429   Median :2.000  
 Mean   :12488   Styria       : 8142   1      : 8602   Mean   :1.943  
 3rd Qu.:18719   Tyrol        : 4796   5      : 6745   3rd Qu.:2.400  
 Max.   :25000   Carinthia    : 4111   6      : 2094   Max.   :4.500  
                 (Other)      : 8511   (Other): 1476                  
    eqIncome           pid            id                 age       
 Min.   :     0   Min.   :1.00   Length:58654       Min.   :-1.00  
 1st Qu.: 13539   1st Qu.:1.00   Class :character   1st Qu.:22.00  
 Median : 18322   Median :2.00   Mode  :character   Median :40.00  
 Mean   : 20163   Mean   :2.07                      Mean   :39.75  
 3rd Qu.: 24277   3rd Qu.:3.00                      3rd Qu.:57.00  
 Max.   :179946   Max.   :9.00                      Max.   :97.00  
                                                                   
    gender         ecoStat      citizenship       py010n           py050n      
 male  :28539   1      :20900   AT   :44066   Min.   :     0   Min.   : -6895  
 female:30115   5      :12836   EU   : 1257   1st Qu.:     0   1st Qu.:     0  
                7      : 4607   Other: 3162   Median :  2382   Median :     0  
                2      : 4362   NA's :10169   Mean   :  9062   Mean   :  1288  
                4      : 2921                 3rd Qu.: 16820   3rd Qu.:     0  
                (Other): 2859                 Max.   :199075   Max.   :129874  
                NA's   :10169                 NA's   :10169    NA's   :10169   
     py090n            py100n           py110n            py120n        
 Min.   :    0.0   Min.   :     0   Min.   :    0.0   Min.   :    0.00  
 1st Qu.:    0.0   1st Qu.:     0   1st Qu.:    0.0   1st Qu.:    0.00  
 Median :    0.0   Median :     0   Median :    0.0   Median :    0.00  
 Mean   :  444.6   Mean   :  3713   Mean   :   72.9   Mean   :   51.22  
 3rd Qu.:    0.0   3rd Qu.:     0   3rd Qu.:    0.0   3rd Qu.:    0.00  
 Max.   :29887.1   Max.   :101777   Max.   :22546.8   Max.   :46398.44  
 NA's   :10169     NA's   :10169    NA's   :10169     NA's   :10169     
     py130n            py140n             hy040n             hy050n      
 Min.   :    0.0   Min.   :    0.00   Min.   : -2962.5   Min.   :-11857  
 1st Qu.:    0.0   1st Qu.:    0.00   1st Qu.:     0.0   1st Qu.:     0  
 Median :    0.0   Median :    0.00   Median :     0.0   Median :     0  
 Mean   :  393.7   Mean   :   41.73   Mean   :   879.9   Mean   :  2826  
 3rd Qu.:    0.0   3rd Qu.:    0.00   3rd Qu.:     0.0   3rd Qu.:  4558  
 Max.   :53183.6   Max.   :18643.46   Max.   :129586.6   Max.   :118309  
 NA's   :10169     NA's   :10169                                         
     hy070n             hy080n             hy090n              hy110n        
 Min.   :    0.00   Min.   :     0.0   Min.   :  -457.46   Min.   :    0.00  
 1st Qu.:    0.00   1st Qu.:     0.0   1st Qu.:     0.75   1st Qu.:    0.00  
 Median :    0.00   Median :     0.0   Median :    58.45   Median :    0.00  
 Mean   :   93.12   Mean   :   744.6   Mean   :   462.45   Mean   :   32.97  
 3rd Qu.:    0.00   3rd Qu.:     0.0   3rd Qu.:   234.78   3rd Qu.:    0.00  
 Max.   :17954.97   Max.   :124206.2   Max.   :112011.03   Max.   :14506.49  
                                                                             
     hy130n          hy145n            main        
 Min.   :-5490   Min.   :-29519.3   Mode :logical  
 1st Qu.:    0   1st Qu.:  -256.8   FALSE:33654    
 Median :    0   Median :     0.0   TRUE :25000    
 Mean   :  339   Mean   :  -108.8                  
 3rd Qu.:    0   3rd Qu.:     0.0                  
 Max.   :40763   Max.   : 49768.0

5. Data preparation

  • Filter for South Austria regions (Styria and Carinthia)
  • Keep only positive income observations
  • Convert household size to numeric
  • Remove missing values
  • Group citizenship categories if needed
dat <- eusilcP %>%
  select(py010n, gender, citizenship, hsize, age, region) %>%
  filter(region %in% c("Carinthia", "Styria")) %>%
  filter(py010n > 0) %>%
  na.omit()

dat$gender <- as.factor(dat$gender)
dat$citizenship <- as.factor(dat$citizenship)
dat$hsize <- as.factor(dat$hsize)

model_int <- lm(py010n ~ gender * citizenship + hsize + age, data = dat)
anova(model_int)
summary(model_int)

Call:
lm(formula = py010n ~ gender * citizenship + hsize + age, data = dat)

Residuals:
   Min     1Q Median     3Q    Max 
-23632  -5930  -1065   4652  95265 

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                   15907.30     589.59  26.980  < 2e-16 ***
genderfemale                  -7711.77     271.54 -28.400  < 2e-16 ***
citizenshipEU                  1487.22    1520.96   0.978   0.3282    
citizenshipOther              -5343.40     987.60  -5.410 6.56e-08 ***
hsize2                         -220.35     461.65  -0.477   0.6332    
hsize3                         -606.41     445.42  -1.361   0.1734    
hsize4                        -1072.25     468.18  -2.290   0.0220 *  
hsize5                         -809.71     567.70  -1.426   0.1538    
hsize6                        -3380.42     686.65  -4.923 8.78e-07 ***
hsize7                        -2815.78    1425.09  -1.976   0.0482 *  
hsize8                        -4156.36    1633.33  -2.545   0.0110 *  
hsize9                        -1552.22    1650.84  -0.940   0.3471    
age                             132.13      10.37  12.741  < 2e-16 ***
genderfemale:citizenshipEU      161.21    2161.44   0.075   0.9405    
genderfemale:citizenshipOther   874.02    1517.33   0.576   0.5646    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9517 on 5252 degrees of freedom
Multiple R-squared:  0.1766,    Adjusted R-squared:  0.1744 
F-statistic: 80.44 on 14 and 5252 DF,  p-value: < 2.2e-16
qqnorm(residuals(model_int))
qqline(residuals(model_int))

plot(allEffects(model_int))

6. Descriptive statistics

6.1 Numeric summaries

summary(dat$py010n)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
     1.93  10066.01  16225.84  16952.35  21939.78 118362.27 
summary(dat$age)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  16.00   29.00   40.00   39.73   49.00   97.00 
summary(dat$hsize)
   1    2    3    4    5    6    7    8    9 
 679 1140 1454 1105  496  274   48   36   35

6.2 Frequency tables

table(dat$gender)

  male female 
  3004   2263 
table(dat$citizenship)

   AT    EU Other 
 5021    79   167

7. Univariate visualizations

7.1 Employment income (py010n)

ggplot(dat, aes(x = py010n)) +
  geom_histogram(bins = 50) +
  labs(title = "Histogram of employment income (py010n)")

ggplot(dat, aes(y = py010n)) +
  geom_boxplot() +
  labs(title = "Boxplot of employment income (py010n)")

7.2 Age

ggplot(dat, aes(x = age)) + geom_histogram(bins = 30)

ggplot(dat, aes(y = age)) + geom_boxplot()

7.3 Household size (hsize)

ggplot(dat, aes(x = as.numeric(hsize))) +
  geom_histogram(binwidth = 1) +
  labs(title = "Histogram of Household Size")

ggplot(dat, aes(y = hsize)) + geom_boxplot()

7.4 Gender

ggplot(dat, aes(x = gender)) + geom_bar()

7.5 Citizenship

ggplot(dat, aes(x = citizenship)) +
  geom_bar() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  labs(title = "Frequency of citizenship")

8. Bivariate plots (predictors vs response)

8.1 Gender vs income

ggplot(dat, aes(x = gender, y = py010n)) +
  geom_boxplot() +
  labs(title = "Income vs gender")

8.2 Citizenship vs income

ggplot(dat, aes(x = citizenship, y = py010n)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  labs(title = "Income vs citizenship")

8.3 Age vs income

ggplot(dat, aes(x = age, y = py010n)) +
  geom_point(alpha = 0.3) +
  geom_smooth() +
  labs(title = "Income vs age")

8.4 Household size vs income

ggplot(dat, aes(x = hsize, y = py010n)) +
  geom_point(alpha = 0.3) +
  geom_smooth() +
  labs(title = "Income vs household size")

9. Interaction plots

9.1 Gender × Citizenship

ggplot(dat, aes(x = gender, y = py010n, fill = citizenship)) +
  geom_boxplot(position = "dodge") +
  labs(title = "Income interaction: gender × citizenship")

9.2 Age × Gender

ggplot(dat, aes(x = age, y = py010n, color = gender)) +
  geom_point(alpha = 0.3) +
  geom_smooth() +
  labs(title = "Income interaction: age × gender")

9.3 Age × Citizenship

ggplot(dat, aes(x = age, y = py010n, color = citizenship)) +
  geom_point(alpha = 0.3) +
  geom_smooth() +
  labs(title = "Income interaction: age × citizenship")

9.4 Household Size × Gender

ggplot(dat, aes(x = hsize, y = py010n, color = gender)) +
  geom_point(alpha = 0.3) +
  geom_smooth() +
  labs(title = "Income interaction: hsize × gender")

9.5 Household Size × Citizenship

ggplot(dat, aes(x = hsize, y = py010n, color = citizenship)) +
  geom_point(alpha = 0.3) +
  geom_smooth() +
  labs(title = "Income interaction: hsize × citizenship")

10. Contingency tables (categorical × categorical)

table(dat$gender, dat$citizenship)
        
           AT   EU Other
  male   2867   40    97
  female 2154   39    70
  • If categories are too detailed, merge small ones:
dat$citizenship <- fct_lump(dat$citizenship, n = 3)
table(dat$gender, dat$citizenship)
        
           AT   EU Other
  male   2867   40    97
  female 2154   39    70

extra ggplot(dat, aes(x = age, y = py010n)) + geom_point(alpha = 0.3) + geom_density_2d(color = “blue”) + labs(title = “Income vs Age with 2D Density Contours”, x = “Age”, y = “Net Employment Income (py010n)”)

extra ggplot(dat, aes(x = age, y = py010n)) + geom_point(alpha = 0.3) + geom_density_2d(color = “blue”) + labs(title = “Income vs Age with 2D Density Contours”, x = “Age”, y = “Net Employment Income (py010n)”)

Compares income distributions across citizenship groups, separately for men and women.

Highlights potential interaction between gender and citizenship.

11. Summary

  • The income variable is highly right-skewed with outliers.
  • Men typically have higher median employment income than women.
  • Citizenship differences may indicate structural inequality in wages.
  • Age and income show a nonlinear increasing pattern.
  • Larger households do not clearly correlate with higher or lower income.
  • Some interaction effects appear visible (gender × citizenship, etc.).

END OF DOCUMENT